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The phrase "a first tranche of" is correct and usable in written English.
It is typically used in financial or project management contexts to refer to an initial portion or installment of a larger amount or series.
Example: "The company has secured a first tranche of funding to begin the development of the new product line."
Alternatives: "an initial portion of" or "a preliminary installment of".
Exact(22)
A first tranche of £470,000 was awarded by City Bridge Trust in May this year.
On Monday a first tranche of ballot papers for the contest will land on doormats and drop into email accounts.
Victims have received a first tranche of cash, but there are fears that additional payments will be cut short if further donations by retailers are not forthcoming.
The UAE this month launched an international research prize for weather modification, awarding a first tranche of $5m to researchers from Germany, Japan and the UAE.
On July 28 the IMF agreed to grant a $14.9 billion loan to Ukraine, with a first tranche of $1.89 billion provided immediately and the remainder dispersed in quarterly installments.
After approving a first tranche of €10.3bn this spring, of which €7.5bn has so far been released, the 19 finance ministers are due to disburse the rest this month but might withhold payment for the rest of the year.
Similar(38)
The price of shares in Deutsche Telekom, a third tranche of which was sold a year ago for euro66.50 ($63.90), dipped below euro17 this week, a mere euro2-odd more than the price of the first initial public offering in 1996.
In addition, it qualified for a second tranche of $1 billion from the U.S. Millennium Challenge Account.
A second tranche of emails was uploaded onto the internet late last year.
Prosecutors are now preparing a second tranche of four similar cases.
Criminal solicitor fees are due to fall by a second tranche of 8.75%.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com